## The Kohn-Sham equation of state for elemental solids: a solved problem

### Abstract

The success of modern density-functional approximations to electronic-structure theory has led to a wealth of

general-purpose codes, allowing researchers to tackle a wide range of applications. Given this extensive usage

by the scientific community, it is striking that it has never been thoroughly investigated to what extent results

vary over different implementations: do different approaches to density-functional theory really yield identical

predictions for a given exchange-correlation functional? We report the results of a community-wide effort that

compares 15 different codes using 40 different potentials or basis set types to assess the quality of the Perdew-

Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that codes and pseudopotential

datasets have only recently achieved error bars of 1-2 meV/atom for solids. Hence, we have only now come to

a level where the differences between most implementations of the Kohn-Sham equations for a given functional

are comparable to the uncertainty in a high-precision experimental determination of the equation of state.